This quest is encountered in the quest-lines of both the Imperial and the Stormcloak factions of the civil war in Skyrim. There are slight differences depending on which side you are allied with.
The city of Whiterun has strategic value for both the Imperials and the Stormcloaks. It is time for the Jarl of Whiterun to declare whose side he is on in this conflict, and the leader of your side will send you to get that answer from him.
If you are on the side of the Imperials
Speak with General Tullius in Solitude after delivering him the Jagged Crown. He will tell you to deliver a message to Jarl Balgruuf of Whiterun.
IMPORTANT: you must have completed the quest Dragon Rising in the main quest before being able to complete this quest.
Go to Whiterun, find the Jarl in the stronghold known as Dragonsreach and deliver Tullius’ message. Jarl Balgruuf will converse with Irileth and Proventus Avenicci, and he decides to declare for the Imperials in the civil war. He will give you Balgruuf’s War Axe, and ask you to deliver it to Ulfric Stormcloak in the Palace of the Kings in Windhelm, to signify that there is to be war.
When you do this, Ulfric will tell you to return to Whiterun and give Jarl Balgruuf back his axe. Upon return, Balgruuf will not be surprised that Ulfric returned the axe, and he has already requested that Tullius dispatch Legionaires to help defend Whiterun. Legate Quentin Cipius will be in Dragonsreach, and you need to report to him to end this quest and begin the next one.
If you are on the side of the Stormcloaks
Speak with Jarl Ulfric Stormcloak at the Palace of the Kings in Windhelm after bringing him the Jagged Crown. He will tell you that it is time to deliver a message to the Imperialists of Whiterun and give you Ulfric’s War Axe to deliver to Jarl Balgruuf the Greater of Whiterun.
Travel to Whiterun and speak with Jarl Balgruuf. Following a conversation, he will give you back the axe, signifying his defiance. He has sided with the imperials and there is to be war with Whiterun. Travel back to the Palace of the Kings to give Ulfric Stormcloak the news.
Upon completion of this conversation you may have to wait or exit the palace and come back in again. Upon your re-entry, Ulfric Stormcloak will initiate a scripted event in which he will ask you to report to Galmar Stone-Fist. Speaking to Stormcloak this second time will finish this quest and start the next one.